E=mc^2 may be the most famous equation in the world… but what you might not know is

that it isn't the whole story. It just describes objects that have mass and that aren't moving.

The full equation is E, squared, equals m c squared, squared, plus p times c, squared,

where p represents the momentum of the object in question. This might all seem a bit confusing,

but in fact you can draw it as a right triangle with sides E, m c squared, and p times c - and

just use the pythagorean theorem (a squared plus b squared equals c squared) to give you

the equation.

Also, from here it's clear to see that for an object that isn't moving and thus doesn't

have any momentum and thus p is zero, we get back our good ole' friend E=mc2. On the other

hand, if the particle in question is massless (like light), then mass is zero and we get

E equals p times c. This tells us that the energy of a massless particle (like a photon

of light) is the same as its momentum (up to a factor of the speed of light).

In fact, the closer the energy of something is to p times c, the closer that something

is to behaving like light (I mean, look here, this tiny little bit of mass is hardly mass

at all).

Anyway, as an example, an object's velocity is equal to the speed of light times the ratio

of the object's momentum to energy - or pc over E. If your momentum increases, p times

c gets closer and closer to equaling your energy, so their ratio gets closer and closer

to being one, and your speed gets closer and closer to light speed. But because of that

tiny little bit of mass, the momentum side of the triangle will always be a little bit

smaller than the energy side. No matter how hard you try to increase your momentum, it

never quite gets to the point where p times c equals your energy, and thus your velocity

can never quite reach the speed of light, all because the hypotenuse of a right triangle

is longer than its legs.